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A selection lemma for Ky Fan's coverings is first proved, and then applied together with Ky Fan's generalization of the classical Knaster-Kuratowski Mazurkiewicz theorem to obtain a new covering theorem of simplexes. As applications, results on the consistency for certain systems of linear inequalities are obtained. 相似文献
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Mau-Hsiang Shih Kok-Keong Tan 《Journal of Mathematical Analysis and Applications》1985,108(2):333-343
Let E be a Hausdorff topological vector space and X ? E an arbitrary nonempty set. Denote by E′ the dual space of E and the pairing between E′ and E by 〈w, x〉 for w?E′ and x?E. Given a point-to-set map S: X → 2X and a point-to-set map T: X → 2E′, the generalized quasi-variational inequality problem (GQVI) is to find a point and a point such that for all . By using the Ky Fan minimax principle or its generalized version as a tool, some general theorems on solutions of the GQVI in locally convex Hausdorff topological vector spaces are obtained which include a fixed point theorem due to Ky Fan and I. L. Glicksberg, and two different multivalued versions of the Hartman-Stampacchia variational inequality. 相似文献
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A topological proof (via the generalized Gelfand spectral radius formula) is given of the fact that every compact set of complex n×n matrices admits a König chain. 相似文献
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In this paper we use a fixed-point theorem of the Ky Fan typewhich is proved by J.-P. Aubin to give a common generalizationof two matching theorems of Ky Fan concerning closed coveringsof convex sets in topological vector spaces. 相似文献
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Certain types of integral inequalities which were established by LaSalle, Gollwitzer, Langenhop, Bondge, and Pachpatte are reviewed and unified. The bounds provided by these inequalities can be used in the study of the theory of partial differential and integral equations. 相似文献
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